Problem: What is the positive difference between the two solutions of $|x + 5| = 20$?
Answer: Let the two solutions to the equation be $x_1$ and $x_2,$ where $x_1>x_2. $ It follows that  \[x_1 - x_2 = (x_1+5)-(x_2+5) = 20 - (-20) = \boxed{40}.\]